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EC349 Financial Economics 2022-2023 SET EXERCISE

1. Assume a perfect capital market under certainty and answer the following questions.

a)   A single-owner firm faces a two-period planning problem with the transformation curve (K1  + 4)2  + K2(2)  = 25 and initial resources equalling 1. Assume the market interest rate is 5%. Work out the firm’s initial wealth maximization problem and illustrate your answer in a diagram.  [5 marks]

b)   What happens if the market interest rate increases? When does the firm stop borrowing from the capital market in time 1? Explain, calculate, and illustrate your answer on top of the same diagram used in a). [5 marks]

c)   Suppose the owner ofthis firm has the utility function of U = c1 with no other income or wealth. Using the same market interest rate of 5% and results from a), work out the utility maximisation problem and illustrate your answer on top of the same diagram. [5 marks]

d)   Now a proportional transaction fee is applied when this individual borrows from the capital market for consumption purposes. Assume this percentage is equivalent to the last non-zero digit of your student ID – i.e., if your student ID ends with 7, this means the transaction fee equals 7% of the amount borrowed, and if your student ID ends with 90, then 9%, and if your student ID ends with 300, just take 3%, etc. Work out the utility maximisation problem with this new constraint, explain what happens to optimal choice of c1 and c2, and illustrate your answer on top of the same diagram. [10 marks]

2. Assume you have the following von Neumann-Morgenstern utility function:            U(w) = 40000 − (200 − )2 where w denotes wealth measured in pounds.

a)   Work out the utility maximisation problem and illustrate the answer in a diagram. [5 marks]

b)   Explain what Arrow-Pratt coefficients of absolute risk aversion (ARA) and relative risk aversion (RRA) seek to measure. [5 marks]

c)   Find  out  the  values  for  ARA  and  for  RRA  for  this  utility  function.  How  does  the individual’s risk attitude vary with the change of their wealth? [5 marks]

d)  Your friend believes that Italy will not win the World Cup while you think that there is a 75% probability that it will. Your friend is willing to pay you x pounds if Italy wins and you pay your friend x pounds if it does not. Your current wealth is £80,000. How much should you bet to maximise your utility? Illustrate in a diagram. [10 marks]

For simplicity and convenience of calculation, suppose there are only one risk-free asset with a return of 5%, and two risky assets, Stock A and Stock B. Information on A and B are summarised in the table below.

Stock A

Stock B

Expected return (%)

10

8

Standard deviation (%)

20

10

Correlation

Use the last two digits of your student ID and divide the number by  100 to get the correlation coefficient. For example, if your ID ends with 85, the correlation coefficient is 0.85. Note: if you ID ends with 00, use the third-last and second-last digits instead to work out the correlation coefficient (e.g., if ending in 300, the coefficient would be 0.3).

a)   Explain the concept of the minimum-variance portfolio (excluding the risk-free asset). Calculate the investment weightings, expected return, and risk of the minimum-variance portfolio of this 2-stock portfolio. Illustrate your answer in a diagram. [5 marks]

b)   Now  include  the  risk-free  asset.  Assume  your  mean-preference  utility  function  is U (E (p), GP) = E(p) − Gp(2) ,  where γ is the last digit of your student ID. Explain the concept of the optimal portfolio, calculate the investment weightings, expected return, and risk, as well as the corresponding utility level, of the optimal portfolio. Illustrate your

answer on top of the same diagram used in a). [10 marks]

c)   Assume there are no other risky assets. What would be the market portfolio? Calculate expected return and standard deviation for the market portfolio. Illustrate your answer on top of the same diagram. [5 marks]

d)   Assume the simple CAPM holds for stocks A and B. What is the beta for your optimal portfolio in b) and for the market portfolio in c)?  Illustrate your answer using a security market line. [5 marks]

4. Short essay. There are some problems with the original CAPM model, and various extensions have been  developed to  address these issues, for  example, the Intertemporal  CAPM, the International CAPM, the Behavioural CAPM, etc.  Choose one extension to focus on. Explain the main idea ofthat extension, and appraise its empirical validity using good-quality references. Word limit for Q4: maximum 800 words, excluding tables, diagrams, equations, direct quotes, and reference list. You must note your word count at the end of your answer. [25 marks]

First > 80%

First >70%

2:1

60 69%

2:2

50 59%

3rd

40 49%

Fail

<40%

Criterion not

relevant to

assignment

Relevance

Totally relevant to the

question set.

Almost wholly relevant to the question set.

Largely relevant to the question set.

For the most part, relevant to the question set; may    be some irrelevant             digressions.

Only partially relevant to the question set .

Largely or wholly irrelevant to the question set.

Depth-Detail

Extensive discussion of   the main issues. Excellent knowledge and depth of   understanding of relevant theories and concepts.

Detailed discussion of the main issues.          Excellent knowledge  and depth of                understanding of         relevant theories and   concepts.

Clear discussion of main issues. Secure knowledge and

good depth of

understanding of

relevant theories

and concepts.

Identification and some    discussion of main issues. Reasonable knowledge    and understanding of       relevant theories and        concepts.

Significant issues not         identified or discussed.      Superficial knowledge and understanding shown.

Shows little or no knowledge and understanding of the main issues.

Engagement with Literature and Sources

Excellent understanding of empirical

literature/economic        theory/policy used, that have gone much beyond the material taught.

Excellent understanding of the empirical             literature/economic        theory/policy used, that have gone beyond the    material taught.

Good understanding of empirical             literature/ economic theory/policy used,  that have gone         beyond the material taught.

Some understanding of empirical

literature/economic      theory/policy used, but has not gone much       beyond the material     taught.

Limited understanding of the empirical

literature/economic        theory/policy used, that has not gone beyond the material taught

Limited or no understanding of empirical

literature/economic           theory/policy, that has not gone beyond the material taught.

Application

and Analysis

of Evidence

and Theory

Excellent integration of economic theory,            empirical literature and  policy (where relevant), with critical analysis of  literature which has both breadth and depth.

Excellent integration of economic theory,          empirical literature and policy (where relevant), with critical analysis of literature.

Very good                integration of           economic theory,     empirical literature  and policy (where    relevant), with some critical analysis of   literature.

Good integration of      economic theory,           empirical literature and policy (where relevant), although discussion of  literature is more           descriptive than critical.

Limited integration of    economic theory,            empirical literature and   policy (where relevant);  discussion of literature is more descriptive than     critical and/or is limited

Little or no integration of   economic theory, empirical literature and policy (where relevant), and little or no     discussion of literature.

Structure,

style and

presentation

Excellent overall               organisation and structure. Excellent links between    components giving a very strong and logical flow to the overall argument.

Excellent presentation, with an effective   &